In modern container transport, a container vessel typically serves/calls a sequence of ports, typically a cyclic sequence of ports. Such a cyclic sequence of ports that a vessel calls will also be referred to as a string, and each voyage of the vessel is referred to as a round-trip (or rotation) through the ports.
A container vessel typically accepts containers at each port of call which are destined for respective ones of the other ports of call that the ship is due to visit. At each port of call, the vessel discharges all of the containers destined for that port and it loads all the containers which are destined for other ports of call which the ship is due to visit.
There are a large number of different types of containers that are transported by container vessels. Typically, standard containers are either 20′ or 40′ long, 8′ wide, and 8′6″ high. The capacity of a container vessel is normally measured in twenty feet equivalent units (TEU) or forty feet equivalent units (FEU). Non-standard containers include 45′ containers that are 45′ long, high-cube containers that are 9′6″ high, and several types of pallet-wide containers that are a few centimetres wider to accommodate standard pallets inside. Moreover, reefer containers need power supply, out-of-gauge containers (OOG) may have cargo sticking out of one of the gates, and open-top containers may have cargo out of the top. Containers with dangerous goods are handled according to IMO rules that define legal ways to store these containers.
A container vessel typically includes a number of bays where single rows of 40′ or 45′ containers or double rows of 20′ containers can be stacked in respective stacks. Typically, a number of hatch covers divide the bays into under and over deck positions. The levels of containers in a vertical direction within a stack are generally referred to as tiers.
A stowage plan is an allocation plan that allocates/assigns containers to be loaded at a port to positions on the vessel. For the purpose of the present description, the term position is intended to refer to a position on a vessel suitable for receiving a cargo item, such as a container. In general, a valid stowage plan should satisfy certain constraints including the packing rules of the vessel. Examples of such packing rules include physical constraints for the packing of containers, safety constraints, and support constraints, e.g. with respect to reefer containers which typically require a position with power supply.
It is generally desirable to provide a valid stowage plan that minimizes or at least reduces the time at berth and/or other contributions to a cost function. For example, this can be achieved by:                Minimizing the makespan of the quay cranes by ensuring that each quay crane approximately has the same work load,        Minimizing the total number of loads and unloads of containers. In particular this can be achieved by reducing the number of overstows. A container p overstows a container q in a stack if p is above q and q is destined to an earlier discharge port than p,        Minimizing the total number of hatch-lifts and crane moves between bays.        Minimize the number of times cranes must boom to pass the pilot house.        